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W. L. GUMPRECHT.

CQNBINED TvPEwmTlNG AND COMPUTING MACHINE.

APPLICATION FILED FEB-M1916.

Patented Apr. 27, 1920.

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WITNESSES @46M MQW BY ATTu NEY.

W.Ll GUMPRECHT. COMBINED TYPEWNITING AND coMPuTlNG MACHINE.

APPLICATIONAFILED FEB. I, 1916. 1,338,012. Y Patented Apr. 27, 1920.

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W. L. GUMPRECHT. comrNED TYPEWRITING AND COMPUTING MACHINE.

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COMBINED TYPEWRITING AND COMPUTING MACHINE.

APPLICATION FILED FEB. l, 1916- 1,338,012. Patented Apr. 27, 1920.

9 SHEETS-sain 4.

INVENTOR:

ATTO NEY.

w. L. GUMPRECHT. COMBINED TYPEWRITING AND COMPUTING MACHINE. APPLICATION FILED FEB. I, I9'I6. 1 ,338,012, Patented Apr. 27, 1920.

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W. L. GUMPHECHT.

COMBINED TYPEWRITING AND COMPUTING MACHINE.

APPLICATION FILED FEB. I. I9I6.

Patented Apr. 27, 1920.

9 SHEETS-SHEEI 6.

W. L. GUMPHECHT. COMBINED TYPEWRITING AND CUMPUTING MACHINE.

APPLICATION FILED FEB-1.1916.

I INVENTRI ATTORNEY.

W. L. GUMPHECHT.

COMBINED TYPEWRITING AND COMPUTING MACHINE.

APPLICATION FILED FEB. I, 1916.

Patented Apr. 27, 1920.

SHEETS-SHEET 3.

INVENTUM @Mmbw W. L. GUMPRECHT. COMBINED TYPEWRITINC AND COMPUTING MACHINE.

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WILLIAM L. GU'MPRECHT, 0F HARTFORD. CONNECTICUT, ASSIGNOR TO UNDERWOOD COMPUTING MACHINE COMPANY, 0F 'NEW YORK, N. Y., A CORPORATION 0F N'EW YORK.

Specification of Letters Patent.

Patented Apr. 27, 1920.

Application led February l, 1916. Serial No. 75,542.

To all 'lv/1.0m `it may concern .Be it known that I, WILLIAM L. GuitrnEoH'r, .a subject -of the King of Great Britain, residing in Hartford, in the county of Hartford and State of Connecticut, have invented certain new and useful Improvements in Combined Typewritino and Com puting Machines, of which the lfollowing is a s ecification.-

his invention relates to combined ty ewriting and computing machines of the l n derwood-Hanson type, in which pins are set up by the actuation ofthe numeral keys, and subsequently employed to rotate the dial wheels of a register or computing head,A as illustrated and described in United States patent to Hanson, No. 905,421, dated December 1, 1908, and pending ap lication of-F. A. Hart, Serial No.- 466,836, fi ed December 10, 1908, (now 4Patent No. 1,270,411, dated June 25, 1918,) and is illustrated as'an improvement on the applications of Hans Hanson, Serial No. 733,940, filed November 29, 1912; and SerialNo; 626,550, filed May 11, 1911, (now Patents No. 1,279,688, dated September 24, 1918, and No. 1,278,812, dated' September 10, 1918.) l

The object of the present invention is to improve the computin mechanism in this general'class of machines, with a view to providing a sim le mechanism, adapted to be easil operate by the typist, and to eil'ect both a dition and subtraction according to the British monetary standard.

In machines of the Underwood-'Hanson type, the typewriter numeral keys are adaptcd to set computation or index pins arranged upon rack-bars' which mesh with pinions connected Vto the dial wheels, sothat said pins may determine the extents to which the dial wheels are-driven. The general system of subtraction employed in the resent disclosure is analovous to that set orth in the application of 626,550, filed May 11, 1911, wherein it is found advantageous to do subtractionby the complementary method. In the complementary method of subtraction, the numeral wheels may'always turn in the same direction, and subtraction is effected by turning cach wheel additivel to an extent ual to the complement of t e number it is esired to subtract.

Hcretofore it has been supposed that in l:Hans Hanson, Serial No.

sterling machines it was practically essential to have a special key for the .writing und computing of pence exceedin .9?. Ac coi-fling to the present invention, a l the computing in every denomination may be effected by the usual ten numeral typewriter keys ranging from l to 9. and 0. i It has heen found possible to automatically make all mechanical changes necessary to perform this operation of computing sterling, while at the same time preserving the solid structure which has been found advantageous in the Underwood-Hanson machine, one of the features of said structurebeing that the rack-bars which do the computing may always move on fixed bearings,.thus av0iding the necessity of supporting them by moving parts at any time. To obtain this result, it has been found advantageous to provide a single wheel on 'which all the pence are computed, and to drive this wheel by a single rack-bar. Where addition is to be performed,`the driving of this rackfbar may be suitably modified by means of another bar for computing the pence exceeding 9 in value.

It has also been found advantageous to provide'another bar for drivingthe pence rack-bar when subtraction is to be effected. In this vway it has been found possible to preserve the ordinary pin-setting linkages with their light construction, so'that they may extend entirely. across the machine and set any number of pins simultaneously, without producing a heavy load on the numeral keys of the typewritelythus avoiding the weakness which would result, were the pin-settingbars curved or not continuous across the machine. Iihave Afound it possible to obtain these results vby altering the connectionsof only oneA or two of' the numeral keys' to their respective pin-setting hars, with t 1e result that the machine is not only strong, but simple to repair and simple to build.

To obtain the above indicated results, I have found'it advantageous to provide connections such that the carriage automatically shifts a bar which will enable the cornputmg mechanism in the tens of pence column to automatically take care of whatever connections are necessary in the units of pence column. These connections may be automatically restored to their normal position f4of pence bar, shownf t -.simplicity, the parts being shown in their normal adding position.

Fi 2' is an `enlarged fragmentary sectiona view, taken'from front to rear, showing the mechanism for setting the machine to subtraction, the mechanism for moving the pins 'finto register with the setting mechanism, and the mechanism for restoring the pins to theirnormal` position.

*F ig. 3 is aside view of the tens of shillin' pin bain.` i

b ig.4 is a View of the units of pence pin ar. 1 .Fig 5fisaview of a supplementary bar sed in connection with the units of pence Fig. 6 is a view ofthe farthings pin bar.

Fig. 7 is aview ofthe complementary in bar used `for driving the far-things ial wheel an extra digit distance, in subtraction.

Fig. 8 ,is a plan view of all the pin-bearing rack-bars, asthey appear in the machine. i

'Fig'. 9 is a fragmentary view of the tens e levers attached thereto which are use in addition.

Fig. 10 is a fragmentary plan view of the tens of pence and units of pence pin bars, and showing their relative position when about to de ress the 1 numeral key in tens place wien computing pence.

Fig. 11 isa plan vlew similar to Fig. 10, showing the :action of the parts when adding eleven pence.

-Fig. 12 is a plan view similar to Fig. 11, showing the action of the parts when adding ten pence.

F igf 13 is a fragmentary plan view of the keyboard of a typewriter.

Fig. 14 is a diagrammatic side view,.snow ing the parts when the shift key is dcpressed to move the platen to upper-case position, the computing mechanism being disconnected from the typewriter.

Fig.15 is a fragmentary side view of the supplementary bar for driving the pence wheel, shown near the end of its forward stroke.

Fig` 16 is a side view similar to Fig. 15, showing the supplementary bar at the beginning of its return stroke, its interponent lever being restored to normal position.

Fig. 17 is a plan view of the pin-setting linkages and connected parts, the parts bcinf shown in subtraction position.

tF ig. 18 is a sectional view, lookin toward the rear, on the line 18-18 of ig. 17, showing the linkage normally associated with the 8 numeral key.

Fig. 19 is a fragmentar erspective view, looking from the rear, ofytlie tens of pence har and associated pin setting linkages showing the parts when the 1 numera key is about to be depressed, in a subtraction computation, to print and compute 1 in tens of pence place.

Fig. 2O is a view similar to Fig. y19 showing the action of the parts during lthe depression of the 1 numeral key to :print and compute 1 intens of pence placel Fig. 21 is a perspective view, looking from the rear, of the pin bars usedin computing pence. and associated pin-setting linkages, showing the action of the parts when printing 0 and computin 10 in the units of pence column, in su traction, after 1 has been printed in tens of pence column.

Fig. 22 is a side view of the tens of pence bar, showing the levers attached thereto used in performing subtraction.

Fig. 23 is a skeleton perspective view, looking from the rear, showing the platenshift mechanism and its connections to the computing mechanism, the case-shift mechanism being in normal position.

Fig. 24 is a perspectlve view similar to Fig. 23, showixw the position of the parts at the depression of the farthings-shift key, the usual shift key remaining in normal position.

Fig. 25 is an enlarged plan view `of the computingr head or register and associated carry-over mechanism.

Fig. 26 is a sectional side view on the line :Z6-26, showing one of the pounds dial wheels and associated carry-over mechanism.

Fig. 27 is a view similar to Fig. 26, on the line 27--27 of Fig. 25, showing the units of shillings dial wheel. v

Fig. 28 is a view similar to Fig. 26, on the line 28-28 of Fig. 25, showing the tens of shillings dial wheel.

Fig. 29 is a view similar to Fig. 26, on the line 29-29 of Fig. 25, showing the pence dial wheel.

Fig. 3() is a view similar to Fig. 26, taken on the line 30-30 of Fig; 25, showing the farthings dial wheel.

Fig. 3l is a view similar to Fig. 26, taken on the line 31--3l of Fig. 25, showing the extra or complementary Wheel which is used to add 1 to the farthings wheel in subtraction.

Fig. 32 is a development of the dial wheels shown in Fig. 25, showing the arrangement of the numerals on their peripheries and the relative position of their carry-over teeth.

Fig. 33 is an enlarged sectional view of the dial wheels shown in Fig. 25.

Numeral keys 41 and alphabet keys 42 are mounted at the front ends of key levers 43 to rock bell-cranks 44 to swing type-bars 45- provided with lower and u per case type 46,

47, to print on the front si e of a cylindrical platen 48 mounted in the usual platen-shift frame 49 which is slidngly mounted for vertical movement on a typewriter carriage 50. Said typewriter carriage is adapted to travel laterally, step by step, in letter-feeding direction, there' being provided for the purpose a spring barrel 51 which tends to move the carriage from riht to left, said motion being controlled by heels 52, formed on the bars 45, and adapted to move rearwar ly a universal bar 53 which actuates a pair of escapement dogs 54, 55, for engagement with an esca ement Wheel 56 connected to a pinion 57 w ich meshes with a rack 58 on the typewriter carriage 50 (Fig. 1).

Certain of the keys, as will be seen by reference to Fic'. 13, are arranged to print two characters. l:In the case of the 2, 3 and 4 numeral keys, they are also used to print 1/4, 1/2 and 3/4 (of a penny), respectivel corresponding to one, two and threeffart 'n in a computing zone. To enable' the writing of these upper-case characters', the laten frame 49 is shifta-ble vertically, an to accomplish this is provided with a roller 61 on its lower end resting on a rail 62 of a shift frame 63, which is se- .cured to a rock shaft 64, so as to be capable of swinging up and down to lift and drop the platen 48 with its frame 49. To swing the shift frame 63 to move the platen to upper-case position, two shift keys are provided, one at either side of the machine, the

i key 65 at the left of the machine being used when it is desired to compute farthings, and the key 66 is used when it is desired to print upper-case characters without performing any com utation, as will hereinafter appear. The shi keys 65, 66 are mounted at the front ends of shift key levers 67 which have upwardly extending rear extensions 68 and 69, respectivel the extension 68 directly engaging the le rear end of the shift frames 63 (Fig. 23), to swing said frame at the depression of the shift key 65. i

The mechanism thus far described is in itself old and well known in the Underwood typewriter, but coperates with the computing.r mechanism. 4or this purpose, there is provided the usual register or gang of computing wheels, and associate with each computing wheel is a pin bar, forminor a temporary computation register for indexing the amount to which its wheel shall be turned. The pins on the pin bars are normally inoperable bythe numeral keys, because they are out of register with pin-setting devices, to be described below, but as the typewriter carriage travels along it automatically shifts these pin bars, one after another, to put their pins under the control of the numeralkeys, so that the travel of the typewriter carriage determines in what pin bars or denominations the digits of a number shall be set up, and the numeral keys of the typewriter depress or set up pins on the bars to register the digits printed.

To bring this about, there is mounted on the carria e 50, so as to travel therewith, one or more enomination selecting tappets (Figs. 1, 14, 23 and 24), according to the number of computinv zones desired. Each tappet, as it travels m right to left with the carriage, in a computing zone, raises in succession, the front end ofeach one of a series of pin bar selecting jacks 76 (Fig. 1

actuates its one of the usual nest of transposition linkages 82, these linkages being necessary to select the computation members one after another, beginning with the left hand one, becausethe ty ewriter carriage travels from the right. ach of these linka es rocks its bell-crank lever 85, the upwardly extending arms of which levers engage wrists 86 on the rear ends of the pin-bearing bars 95, so that each thrust rod 77 will move forwardly its pin bar into register with a pin-setting mechanism by its lever 85 and thereby determine the denomination in which indexing is to take place. Thus the typewriter carriage determines both the denomination of indexing and printing, as is more fully described in the patent of Frederick A Hart, No. 1,287,301, dated December 10, 1918, the connections being such that the pins on said bars are brought seriatm into register with the pin-setting mechanism which will now be described.

The pins on the pin bars are, as intimated above, normally out of register with the pinsettinfr devices, but when any pin bar is movedl into register with said devices, any numeral key 4l is adapted to set its pin 94 on that pin bar 95 by means of a pendent thrust link 90. The connections for doi this include an arm 91. fast to the front e5 of a rock shaft 92, said rock shaft having rigid thereon an upright rock arm 89, adapted to actuate its one of the nest of linkages 93, by moving said linkage downward. The downward movement of any numeral key causes its link 90 to strike its arm 91 to depress the linkage which depresses the corresponding index pin 94 on the pin bar, which at the moment has been moved forward into pin-setting position, all the other pin bars remaining in normal position, so that their pins are not in register with the linkage 93 actuated at the moment.

A general operator including a cross bar 120 (described below), is adapted to drive the pin bars 95, by the projecting ends of the depressed pins so that racks 96 formed at their :forward -ends (Figs. 8 and 26) drive dial pinions 97 loosely mounted on a shaft 98 which supports the dial wheels 99 of the computinghead, said racks constantly meshing with said pinions. The pin or rack bars 95 are adapted to be driven forwardly and rearwardly to rotate their associated pinions in .both directions.

The rack bars are supportedon solid bearings at each end, said bearings being formed by the front` comb 95* and the rear comb 104. These solid bearings make the pin-setting operation easy and certain, because the pin barscannot give or wabble during the pinsetting operation.

In order that the rack bars and their associated dial wheels may rotate idly backward, but Vdrive their wheels when driven forwardly, there is fast on each dial pinion 97 a ratchet 100, the teethvof which engage a spring-pressed plunger 101 (Figs. 26 and 33) mounted on each dial wheel 99, so as to transmit `to the dial wheel the rotation caused by the forward motion of its rack bar 95, through the intermediary of the dial pinion 97, ratchet 100;,and plunger 101, but to allow the teeth of the ratchet-100 to pass theend of the plunger 101 during the return motion of the rack bars 95, the dial wheels being held against accidental rotation during said return motion by spring-pressed detents 102 (Fig. 1), which engage detent pinions 103 fast on the dial wheels, said detent pinions bearing as many teeth as there are digit spaces on the dial Wheels.

The dial wheels are provided with one or more carry-over teeth 106 (Figs. 1, 32, and 26 to 30) of the usual Hanson type, adapted to start or partially rotate their associated carry-oven pinions 107 during the rotation of the dial wheels, to set up or initiate a carry-over action. 1The carry-over is subsequently completed during the rearward idle motion of the rack bars 95, at which time spirally arranged assisting segments 108 engage the partially rotated carry-over pinions 107, to cause a three-point pinion 109 fast to each of the carry-over pinions 107, to engage its detent pinion 103 of the dial wheel of next higher denomination, to rotate said dial wheel one digit distance. The carry-over teeth 106 are so placed on the dial wheels that they will initiate `a carry-over action during the time that the dial wheels turn to 0,, as seen through the usual sight-opening 110 in the casing ,ofthe machine (Fig. 1). This carrying action is more fully described and illustrated `inlatent No. 816,319, issued March 27, 1906, to Hans Hanson.

To drive the rack bars 95 forward, after the pins 94 thereon have been set up, cor'- responding to the number to be computed, there is provided the general operatorreferred to above. To operate this, there is provided outside of the casing of.the computing-mechanism, a general operator handle 114, fast toria rock shaft 115, extending across the machine and journaled in the casing'thereof. ,Fast von said rock shaft, lat

either side of the machine, are gear segments 116, meshing with and adapted todrive pin.- ions 117 at the actuation ofsaid handle .114, said p inions' 117 meshing. with-` horizontally disposed. rack bars `118,4 on either side ofthe machine vand adapted .to move forwardL at" the forward stroke ofthe handle 114. ach rack bar 118 `has I,fast

thereon a bracket 119, uniting it to the cross,

bar or general operator 120, extending across the machine between thebrackets119-and adapted to engage the lower ends of the index pins 94 which have been depressed. On the forward stroke of the handle A114, the general operator bar 1 20 is moved forwardly through the intermediary of the segment 116, pinion 117 and rack 118, to engage the projecting ends of thedepre'ssed pins 94Zand thereby drive forwardly the pin-bearing rack bars 95, on which said pins have been depressed, the racks 96 on the forward end of said rack bars transmitti theirl motion to their respective dial whee s. Thus each dial wheel is rotated a distance corresponding to the value of the numeral key 41 actuated when the typewriter carriage was holding its pin bar in pin-settin position.

0n the return stroke of tie general operator handle 114, the rack bar 118 and general operator 120 are moved rearwardly, the

slidinglyV mounted latter engaging downwardly projectinglugs 123 on the rack bars 95, to carry rearward said rack bars to their normal position, so that another computation may be indexed upon them. y

As hereinbefore described, when a dial wheel 99 is rotated, so that its numeral 0 comes before the sight-opening 110, it will initiate a tens-carrying action, to complete which it is necessary to rotate the carry over assisting segments 108. For this puriose, there is provided as in the Hanson atent, 816,319, aforesaid, in mesh with the forward end of the rack 118, a gear 124, in mesh with a pinion 125, which hasa oneway hall-clutch connection (not shown), with a shaft 126, on which are rigidly mounted the tens-carrying segments 108. The gears 124, 125 and the one-way clutch are constructed and proportioned so as to rotate the carrying segments 108 one revolution in clockwise direction (Fig. 1), to engage any pinions 107, on which a carrying action has been initiated durlng the forward stroke of the general operator, to complete said carrying action.

To restore the index pins 94, which have been depressed ina computation, to their normal ineffective position, there is provided the vusual iii-restoring plate 136, which is actuated y the General operator. For thus actuating the plate, the general operator bracket 119 is provided with a pawl 129, pivoted thereon and drawn against a stop, which limits its forward motion, by a spring 130 (Figs. l and 2). The pawl 129 normally stands at the rear of an arm 131, fast on a rock shaft 132, which carries bell-cranks 133 loose thereon. The downwardly extendin arms of said bellcranks areconnected y a link 134 to the downwardl extending arms of bell-cranks 135. The orwardly extending arms of the bell-cranks 133 and 135 carry a pin-restoring plate 136, pivotally connected thereto and extending under all the'index pins 94 at a suicient distance therebelow to allow said pins to be depressed when said late is in 4normal ineiective position. T e pin-restoring plate is operated as follows At the forward stroke of the general operator, the pawl 129 will move forward idly therewith its upper free end engaging the arm 131 urin the initial part of sai forward stroke, an will be thrust rearwardly about its pivot a inst the tension of the spring 130 until tieL free end of the pawl 129 has passed clear of the arm 131. During this time the restoring plate 136 remains in its idle lower position. Near the rear end of the return stroke of the general operator 120 the free end of the pawl 129 will pass underneath the arm 131; the former being held against actuation by its stop, will force the arm 131 upwardly, to rock'the shaft 132, swin g upwardly an arm 137, fast thereon ig. 1), the rear end of which is adapted to engage an extension on the pin-restoring plate 136, thereb forcinssaid plate upwardly against the ower en of the depressed index pins 94 to carry said pins upwardly to their normal ineli'ective position, the parallel motion of the pin-restoring plate 136 being assured by the bell-cranks 133, 135, and link 134.

. As hereinbefore stated, this machine is adapted to perform addition and subtraction, -according to the British monetary standard. For this purpose, its computing head. pin-hearing rack bars :ind pin-settingr linkages are constructed as follows The dial wheels 99 of the computing head are constructed to display at the sight-opening 110, the result of the computations performed, in pounds sterling, shillings, pence and fractions of pence. For this purpose, each of the dial wheels which indicates pounds sterling has ten numerals equally spaced on its periphery, from 0 to 9 (Figs. 25, and 32), and bears one carryover tooth 106, to initiate a sin le carryover action in one rotation of the rial wheel. The construction and action of these pounds sterling dial wheels is like that of similar dial wheels in a decimalsystem, such as is shown in the Hanson Patent, 816,319, aforesaid. The dial wheel 99, indicating tens of shillings (Figs. 25, 28 and 32), has the numeral 1 e ually spaced live times on its periphery, a lank space being provided between fve successive numerals 1 thereon,

said blank spaces representing Os, and

like numerals, being adapted to appear at the sight-opening 110, as will hereinafter appear. The tens of shillings dial wheel consequently bears five equally spaced carry-over teeth 106, adapted to initiate a carry-over action whenever any numeral 1 on the dial wheel 99' passes from the sight-opening 110. The dial wheel 99, in-

dicatin units of shillings (Figs. 25 and 27) is llocated to the right of the dial wheel 99., as seen in Fi 32, and is constructed like the dial whee s 99 of the pounds sterlino' order.

'he dial wheel 99", for indicating pence (Figs. 25, 29 and 33), consists of two united dial disks 99, 99", indicating at the sightopening 110, tens of ence and units of pence, respectively, an are fast on a common sleeve 140, 'ournaled on the dial wheel shaft like the dial wheels of other denominations. Said sleeve has loosely mounted thereon between said disks 99* and 99" a pinion 97 and ratchet 100 like the other dial wheels. The dial 99" has twelve numerals equally spaced on' its peri hery running from 0 to 9, and also inc uding an extra 0 and an extra l, as seen in Fig. 32. On the dial 99l stand the numerals 1 and 1 to indicate ten and eleven pence, when the numerals are read aero both disks 99* and 99" at the sight-opening the rest of the dial 99l being left blank. the dial when 99l is provided with one carry-over tooth 106, so placed thereon as to initiate a carryover action when the numeral 11 von the combined dial wheel 99 passes from the sight-opening 110.

The dial wheel 99, indicating farthings nr fractions of pence (Figs. 25, 30 and 32), has the numeral fractions 1/4, 1/2 and 3/4. arranged in progressive order on its periphery, each fraction appearing three times thereon, and has a zero o r blank space of one digit distance between the numeral fractions 3/4 and 1/4, as seen in Fig. 32, the fractions U4, 1l/2 and 3/4 beingr equivalent to one, two or three distance equivalent to the farthings. Said wheel may be termed the farthings dial wheel, and is provided with threiarfequallyV spaced carry-over teeth 106, arranged to' initiate a carry-over action when the numeral fraction 3/4 passes from the sightopening 110.

A"In order to rotate each dial wheel one digit distance for every unit in the number wmpted inthe corresponding denomination, index pins' are preferably equally s aced onthe rack bars 95, which drive the ial wheels=99,"'and 'on every' bar are arranged at the same distance fromeach other; Tile rack" bars 95 ofthe ounds sterling order'are 'each rovided withV nine such index i'ns 94., as 1n the ordinary Underwoodanson' machine, arranged in such relation to tle' 'general operator cross bar'120 so that the' l eral "operatorwill move each rack bar' rwardly during its forward 'stroke a digital value of the-de ressed' indeirpn thereon; That is, when-t e foremost 'index pin 94'is enga ed bythe general operator 120, the rack' ar will be moved forwardly to rotate the corresponfdirg dial wheel one digit distance. When thefrearmostpin 94 is depressed, the general operator 120will move t 1e' rack bar 954 forwardly to rotate its corres ending dial wheel a nine digits distance dgl. 8).

Inasmuch as the tens of shi ings dial -wheel F' .28 'is adapted Vto exhibit 0" 'at'.the sig -opening and initiate the tens-carryin action for every two digits distance of.- lts rotation, its associated rack bar '141 i's provided with a single index pi'n 142, adaptedt to be'dcpressed at the actuation'of th'1 numeral key, and placed irrline with the' 1.index pins 94 of the 'unds steriing rack bars 95, so that at t e4 forward strokeof the'general operator, the rack bar 141 will be moved forwardly one digit distance, through the intermedi ary ofthe pin 142, when said pin has been de I' i nasmuch as the units of shillings dial wheel 99 (Fig. 27) is of the same construction as the dial wheels in the pounds sterling order, its associated rack bar 95 is of the same construction as -the rack bars 95 of the' pounds sterling order.

Since the pence dial wheel 99d (Fig. 29) is unitary and is divided into twelve digits distance, it is advantageously driven directly by only a single rack bar 143 (Figs. 4 and 8), which occupies a position, corresponding to unitsof pence in relation to the other pinlbearing bars. This units of pence bar is adapted to Vbe moved forwardly a maximum distance equivalent to eleven digits distance rotation of "the dial wheel 99, namely,-one point less than twelve pence or oneshil'lling. When writing 1 in tens of pencc'pliice in a computing zone in addition, a bar 144 (Figs. V8, 9 and l2) is pending on whether ten o'r eleven pence have been indexed. For the pu ose of coperating thus with the units o nce bar, the tens of pence bar 144 has p1voted, ,onv the rightside thereof, a leverof'the 'first order 145, the forward end of which isadapted to be depressed 'atthe actuation of the 1 numeral key when the latter is depressed, when the typewriter carriage 50 is in tens of pence place in a lcomputing zone.v Unless this lever is depressed,thefgeneraloperator is ineective ontheten's o 'cjbarfbut the depression of' the' lever 45 will f raise the rear end thereof., rockin "a""coact,ng lever 146, also pivotedinterin iate 'its' ends en the bar 144, so as to place theA rear endof said lever 146'i`to the path' of 'the'fgeiierel operator cross bai 120. This'lever is held in' either-*position by a 'spring detent 149.` Said cross4 bar 'wil then engage'the rear end of the lever"146 on its forward stroke, to carry' 'the'bar 144 forwardly therewith and transmit* thereto'aA forward stroke of eleven digits distance. In order to transmit the forward motion of 'this tensbf pence bar 144 tothe units of pe'ncef` rack bar 143, there is prv'idedonthebar 144'a71n or projection 147 (Fig s."9 and 12)"adapte to engage a l'ug148 on' the pencebar' to move the latterv forwardly a ten digitss is tance, to rotateits 'associated pence'v dial wheel 99 a similar distance. The gear 97 of the pence dialwheel99 is so proportioned relative to the' digit'distance' between 105 the pins on the pence rack bar 143 as to rotate said dia-l wheel' ,one digitj distance, fi. e., one twelfth of arotation, for every one digit forward movement of the rack bar 143;

It will'be noted that during 'the' opera- 11"l tion of adding ten en'ce, no pins will be set on the pence rac bar 143 when 0 is printed in units of pence place, as will hereinafter appear, the rack bar 143 in adding ten pence receiving its forward motion from 115 the general operator cross bar 129', exclu.- sively from the tens of pence rack bar 144. The relative position 'of the lug1`48onthe bar 143 and the lng 147 on the bar 144 is such that the latter will move idly forward, 120 prior to its engagement with the bar 143.l a short distance, and after this lost-motion the bar 144 will drive the bar'143 by its lug 147 a distance sntiicient to transmit-to the bar 143 a forward stroke equivalent to a 125 ten digits rotation of the dial wheel 99".

When it is desired to add eleven pence, it is necessary to rotate the dial wheel 99d eleven digits distance. For'this purpose,

of pence place is said computation, indexing will take place, as previously described, on the tens of pence bar 144, viz., the lever 146 is positioned as whenathe 1 numeral key was actuated in tens of pence place in the addition of ten, but, in order to move the rack bar 143 forwardly a distance equivalent to eleven digits rotation of the dial wheel 99", through the intermediary of the rack bar 144, there is provided on the rack bar 143 a speciallyformed 1 ,index pin 150 (Figs. 4,8 and 11), placed thereon and normally in .line with the 1 index pins 94 on the rack bars of higher order. The 'index pin 150 is depressed at the actuation of the 1 numeral key in units ofv pence place, as will hereinafter appear, and is'provided with .a lug 151, normally out of the path of the 4lug` 147 on Ythe bar-144, said lug` 151 being moved into the `path of the lug 147 by the depression of the pin 150. This lug 151 will therefore l'then come Vinto engagement with the-.lug 147 when 'the general operator drives forward the bar 144 and willA cause `:its'rack -bar 143-to be carried 'a distance to cause an eleven digits rotation of the pence dial wheel 99d.

In computing asin le penny nothing is written except the 1 in units place; consequently nothing is indexed except the 1 pin 150 on the units pence pin bar, with the resultf that the general operator drives the pence rack bar precisely as though it were an ordinary decimal rack bar, the lug 151 being ineffective because the tens of pence ba-r is unaffected by the general operator. 'In the saine way, if it is desired to add more than one and less than ten in the units of pence column, any .index pin 94 on the bar 143 is set u by the connections usual on Underwoodanson machines, which have been described above.

ln order to rotate the farthings wheel 99' (Fig. 30) a digit distance corresponding to the numeral printed in farthings place in a computing zone, its associated rack bar 152 is provided with three index pins 94, so placed on the rack bar 152 as to enable said rack bar to be moved forwardly by the generall operator120 one, two or three digits distance, corresponding to the addition of 1/4, 1/2 or 3/4 of a penny, respectively. The index pins on the rack bar 152 are placed in line with the index pins 94 on the bars of higher denomination. For the purpose of preserving the usual typewriter keyboard, the 2 numeral key writes 1/4 penny in upper case and actuates the foremost pin on the rack bar152 (Figs.6 and 8),as will hereinafter appear, when -writing in farthings place on the work-sheet (Fig. 13). The middle and rearmost pins on the bar -152 are correspondingly so placed in line ini relation to the other index pins 94 as to bel-.. 66 depressed at the actuation of the 3 and 4 numeral keys, respectively, said keys being 'adapted to print the fractions 1/2 and 3/4 whenYl` the platen frame 49 is in upper-case position, and when computing in farthings place. The general operator is modified as described below, to rotate the farthings dial wheel 99' the di it distance represented by the pin set by t e numeral key actuated.

When it is desired to rform complementary subtractions, the plus 94, of highest value on every one of the pin bars except the pence bar, have to be depressed before beginning the operation, as hereinbefore mentioned.

For this purpose, there is rovided at the front of the machine (Fig. 1 a subtraction key 158, adapted to be .pressed rearwardly and mounted on a thrust rod 159, the-rear end of which is pivoted to an upright arm 160, fast on a rockshaft 161 (Figs. -1 and 2), on which is mounted arearwardly extendingpawl 162, adapted to. engage and hold,

in forward ineffective position, a subtraction bar163 against the tension of a spring 164. Said subtractionbar is guided at its forward end by a slot 165, formed therein, engaging the general operator rock shaft 115, and guided at its rear end by a slot formed in a plate 166, which forms part of the framework of the machine. The subtraction bar 163 has an abutment 167 formed thereon, which engages the plate 166 on its rearward stroke, to limit its rearward motion when drawn by the tension of itsspring 164, which holds it firmly in eifective position. At the rearward movement of the subtraction key 158, the shaft 161 will be rocked, to force the rear hooked end of the pawl 162 out of engagement with a notch 168 formed in the 'subtraction bar 163, which is drawn rearwardly by the power of its spring 164. This sets the pin of highest digital value on each denomination, and f or this purpose said subtraction bar carries rearwardly a bell-crank 169, pivoted thereto, the hook on the forwardly extending arm of which engages a trigger 170, fast on a rocking frame 171` to depress at the rearward stroke of the subtraction bar 163, a bail 172, which forms part of the framework 171 and overlies the levers 173 which engage the pins 94 of highest order of each of the rack bars, to depress said levers and pins. The upper end of the upright arm of the bell-crank 169 is adapted to engage an adjustable stop 174, so as to swing said bellcrank against the tension of the spring 175 near the end of the rearward stroke of the subtraction bar 163, thus moving the hooked end of said bell-crank downwardly, out of engagement with the trig er 170 of the rocking frame 171. This re eases the rocking framel''l. from its depressed position, during the time that the subtraction bar 163 A described below,

remains in its rearward subtracting position, and enables any of the pins 94, which have been depressed by the ail 172, to be restored to their normal ineective position during indexing of numbers in a subtraction computation, as will presently be described.

As has been indicated above, the pins 94 are set for addition in an indexing operation, by operating the rock shafts 92,..which coperate with the numeral keys and have arms thereon, indicated in general by the reference numeral 89, which actuate the linkages, indicated in general by the reference numeral 93. Certain of these arms and linkages are now referred to specifically, according to their coacting numeral keys and the character of operation to which they correspond (Fig. 17), as arms 1^, 2^, 3^, 4^, 5^s, 6^, 7^, 8^ and 9^, which will engage, in their adding position, respectively, the wrists 1W", 2W^, 3W, 4l, 5W^, 6W^, 7W^,

8, and 9W^, fast on their respective links 71, 8L, and 9L, to swingl 113.2147 3L) 4L, 5L 6L? the upper reach of their respective linkages leftwardly, as seen in Figs. 17 and 1-8, at the depression of the numeral key, to depress the lower reach of said linkage against the tension of its spring 180, through the intermediary of the bell-crank levers .181and 182, formi a parallel motion devlce which is adapte to move the lower reach of said linkage downwardly.

It will be seen that on the depression of a numeral key in addition, except the 0 key, the linkage corresponding to the value of the numeral key depressed will be actuated to depress its corresponding pin 94 on the rack bar 95, which has been moved into position to coperate with the linkages 93.

ln order to set the arm and linkage vmechanism 89, 93, to a subtraction condition, so that the numbers to be computed will be indexed to rotate the dial wheels a digit distance corresponding to the complements of the digits in the number to be computed, as there is provided on each rock shaft 92 a subtraction rock arm which is ineffective while adding but eiective while subtracting. To bring about this result, the subtraction bar`163 (Figs. 1 and 2) is provided with a pin 184 which is adapte at the rearward stroke of the subtraction bar to rock an arm 185, fast on a rock shaft 186, on which is mounted an arm 187 adapted to engage a pin 188 at the rear end of an extension 189 on a rock shaft-shifting bar 190 pivoted at 191, on the framework of the machine (Fig. 17), and extendin across all of the arms 91. The lower end o said shifting bar 190 enters slots 192 formed on all of the rock shafts 92, so as to move them all simultaneously. It will be seen by reference to Figs. 1 and 2 that on the depression of the subtraction key 158 190 will be swung on its pivots the intermediary arm 185, rock shaft 186 and arm 187, to move the lower end of the shifting bar 190 forwardly and carry therewith al of the rock shafts 92 from the Fig. 2 (adding) to the F ig; 17 (subtracting) position, so that the rock arms 1^ to 9^, inclusive, will be shifted out of connection with their corresponding links and become ineffective, while a set of subtraction rock arms" the shifting bar 191, through rock shafts 92 will be brought into coperative engagement with wrists lws, 2W, 3l, 4W', 5, GWS, TWs, SWS, SWS and OWS, respectively. The connections now are such that the depression of a numeral key will actuate :the linkage corres ending to the complement of the value sai numeral key represents. The word complement, however, is not used for theJtrue complement, but for the true complement less one. That is,in ordinary decimal numbers, the true complement of any number lis that number deducted from ten. In the present machine the .typewriter numeral keys, as mentioned above, areeach said to set a complementary pin in subtraction, meaning thereby a pin having a value of one less than the true'complement; Thus, in subtracting pence the 2 key sets up a condition equivalent to setting a 9 pin and vice versa, because 12 is the base o computation and 9 is one less than the true complement of 2 to base 12. f

It will be noted that on the in bars of the pounds sterling order and tlle units of shillings pin bar, all the 9 pins 94, on said rack bars, (i. e., all the pins which represent the indexing of nine in addition), are depressed when the machine is set for subtraction, the depression of said pins representing the complementary indexing of 0. It is, therefore, said pins to its normal position when any other digit on its rack bar is set up. For this pur ose, each of the rock shafts 92 is provide with the usual upright arm 200, normally out of engagement with a Wrist 201, said wrists all being mounted on a universal 9 pin restorin linka e 9m. At the end of the shifting orwarf of the rock shafts 92 in a subtraction-setting action, the arms 200 are brought into engagement with the upper reach of the linkage 9, on which are mountedv the wrists 201, so that at the actuation of any numeral key from 1 to 9, said linkage'will be actuated to depress its lower reach, said lower reach being adapted to depress the rear end of any lever 173 on the pin bar of the denomination in which indexing is ta 'ng place, thereby raising the forward end of said lever and its pin 94, and thus restoring said pin to its of the subtraction bar 163,

necessary to reset each of normal ineffective position simultaneously with the depression of any pin in the same denomination. i

It will be noted b reference to Figs. 3 and 8 that the tens o shillin rack bar 141 bears only one pin 142. Un er the method of computing used in this machine, it is advantageous in subtraction tode ress the pin 142 simultaneously with the epression of the .9 'pins n the bars'of higher order. The'pin 142 in subtractionrepresentin the complement'of 0- for the'tensof shil ings' order. To bring this about, there is provided, (Fig: 3), nearer the rear end of the tens of shlllin bar 141, a lever 202,'the rear end of' w ich normally underlies the pin-setting bail 172, to be depressed at thc actuation of the latter, to raise the forward end of said lever which is connected with a lever 203, also pivoted to the bar 141, to depress the forward end of the lever 203 connected to the pin 142 to de ress the latter.

lVhen printing and sulbtracting 1 in tens of shillinfrs denomination, it is neces-n sary to unset the pin 142 so that 0 t e nothing), which is the complement o 1 in tens of shillings lace, will be indexed on the rack bar 141.' or unsetting the in 142, the forward end of the lever 202 w en the im 141 is inindexinu position (ing. s), is adapted to underlie tie lower reach of the linkage 8Il (which is the linkage o erated by the 1 key in subtraction), so t at the forward end of said lever will be depressed to reset the in 142 at the actuation of the l numeral 'ey. It will be noted by referand the linkage 9 is shown as short, it is advantageous to utilize the linkage 8l' for said purpose, because this Jermts a long' lever 202. It may be noted m passing that the units of shillings rack bar 95 has the numbers to be computed in units of shillings place indexed thereon in subtraction, in the same manner as those indexed on the bars of the `pounds sterling order.

When the typewriter carriage 50 comes to the point in a computing zone when tens of pence is to be computed and printed, the tens of pence bar 144 will be moved forwardly by the tappet 75, as has been described above for the other computation bars or rack bars, so that said bar 144 is in position to coperate with the linkage or pinsetting mechanism 93; Said tens of pence bar, however, has no settable pins thereon, but is utilized nevertheless for controlling subtraction of pence and especially for setting the connections necessary for the subtracting of ten pence and eleven pence.

When it is desired to subtract ten pence the ll and the 0 numeral keys are actuated in succession to print the number 10 on the work-sheet in the' ence columns in the com uting zone. At t e down stroke 'of the l ey in the tens of pence column', its rock shaft 92 will be rocked as usual with its arms 1'L 1s and 200. The arm 1^ will rock idly, being out of engagement with its wrist 1W* because 'of the fact that the rock shaft has been shifted into subtraction position;l The arm 200 will depre'ss 4 the lower bar of the linkage, 9m by engaging with the wrist 201 thereon, and this linkage 9 is utilized for the purpose of computing tens of pence subtractivel for reventing the setting up of anypin gythe 1 key in the units of pence column if eleven pence 'is to be subtracted. This is necessary because,

as will be pointed out below, the, pence bar must remain idle if eleven pence4 is to he 'sub-l this purpose,there is'pi'voted ntlle'te'ns of pence bar 144 (Ei 8,' 9, 19,20, 21" and 22), a lever 207el thevv first order. This" lever is ada ted to prevent the setting of a pin by the 8 linkage on said bar which normally would occur in the next column, because it always occurs if the numeral key "1 is o erated, for subtraction in any column. o prevent such a settin therrock arm 1s on the rock shaft 92 of t e .1I key4 actuates' the"8 linkage by a Aremovable wrist 1W", instead of by the usual type of wrist which is fixed to such a linkage. The actuation of the linkage 9m is caused to move this removable wrist to idle position '85 tracted by the comple;neniia.ry` methodj For'.

when the 1fl`{ey is actuated in this tens position. Therefore, whenever the l key i is operated in this zone, the rear end of the lever 207 is depressed. This rocks the levei` 208 to draw down a draw-link 209, pivoted to said lever at the end o pos-ite from the lever 207, and this draw-li t, being attached to a lever 210, pivoted on the u per reach of the 8 linkage, will swing said) lever 210 at the de re'ssion of the 9 linkage, and thereby shi t the wrist 1ws to ineffective position, this being effected because said wrist is made integral with the opposite end of said lever 210. In addition to this, the actuation of the 1 key in tens of ence column enables the 0 key to restore the 9 pin if actuated in units of pence column. To do this, the

lever 207 sets n1prtsof the mechanism so that the 9m li ge will be actuated if the 0 numeral key is actuated in the units of pence ooluinnf For this purpose, the lever 207, through the above-described draw-link sets an interponent 1 215 'm the path o the rock arm 200. on t e 0 numeral key rock shaft, said arm being adapted to thereby actuate `the 9La linka e. This connecting up of the 0 numeral ey is necessary be- Y 209` and the interponent lug 215 include a lever 211, pivoted on the upper reach of the 8 linkage, which engages the end of the lever 210 by a tongue-and-groove connection, said lever forming part of a quasi parallel motion. device, which includes a link 212 pivotedl to the lower reach of the S linkage, and` also includes a vertical link 212, and this vertical link actuates the lug 215 by means. of a horizontal extension 213, extending rearwardly from the vertical link 212 over the pin-settin linkages and having a short downwa y extending arm forming a pin-and-slot connection 214 with the rear-end of the lug 215, said lug being operated by said pin-and-slot connection, and for the purpose of bein so operated is pivoted-intermediate its en s on the upper reach ofthe 9 pin-resetting linkage.

The lever 207 is held in its effective position even when the tens of pence bar 144 is shifted back from indexing position to its normal position. For this purpose, the top of the front end of the lever 207 which cooperates With the lever 208 is long enough to support said lever 208 in both positions. The rear upturned end of the lever 207 is so short that it can be operated by the SLS linkage only when' in indexing position.

In addition to this special connection to the 9 linkage, the 0 numeral key is adapted to actuate a special pin-setting linkage 216, said linkage being adapted to set its corresponding pin 217 on the front end of the pence rack bar. The purpose ot setting this pin is to cause the pence rack bar to drive its ence wheel thereby to the extent of one digit space, this being done because complementary subtraction in pence requires that the indexing mechanism shall turn the pence wheel onespace, to subtract 10, since ten pence is one. less than eleven ce, and, as pointed out above, the iiiexing mechanism in a machine of the present complementary subtraction` type, turns each numeral, wheel one di its ace less than the true complement (which.V or 10 7 to base 12 is.f2) oi the number to be subtracteck` It will, be rememberedthat the' carry-overA mechanism corrects the error by; giving each numemlnheel ,im extra.

digit space, turning in order to obtainthe l eiective forl everyfnumher, infconrplemeni 1 tary subtraction.E 'xheneedL-tonrthis- ,arises from the factsthat, as pointedpgsaheve, the complements. employed pence-subtraction areI computedironi thog ,127, whereas in ordinary'dcima complementary subtraction, the com lements'are coinfy puted from thebasef. 110 Y In both, kinds of subtraction, however, one unit lis added by thecarry-over mechanism, setlist, as also indicated above, thev meehan-smtis built to enable numeral wheels toubedriven by the pin bars or indexing mechanism to an extent asthoughthe. numbers were the conn Jlements of 9' and 11, respectively.

he dierence between ten and twelve, or, for that matter, between nine and eleven, is 2, and ,therefore means are provided to automatically causev they general operator to always drive the pencerack bar in subtraction two more digitswthan the digits represented by the pins actually set up. For thispurpose, there is provided a supple mentary operator 218, shown in Fig. 5, said o erator being; like the rack bars in gener form, but lacking any teeth, because it. drives the pence wheel exclusively through the pins on the pence pin bar. For this purpose itis provided with a. horizontally extending lug 219 (Figs. 5 and 8), which rides a behind any depressed pence bar pin and will drive said bar by said pin. To do this driving it is adapted` to cooperate with the general operator 120 by means of a. 4lever 223 ivoted on the operator 218, said lever having integral therewith a lug 225, which normally stands clear ot the general ogerator. Said'lug, however, is brought in ront o the general operator whenever the subtraction key 158 is operated, sol that the general operator will drive the supplementary operator 218 by the lug 225 and through the lug 219 give the; pence bar the requiredfextra. drive of twovdigits. To do this, the lever 223 has an upwardly beyond' a extending lug 224 which underlies the universal 9 plu-setting bar 172, with the result that whenever the 9 pin-setting bar 172 is actuated, it thrusts the rear end of the lever 223 downwardly to carry the lug 225 in front of the general operator.

In order to retain the lug 225 in either its el'ective or inetfective position, there is provided a spr detent 234, fast on the operator 218, whic cooperates with suitable openings forlholding the lever 223 in either its idle :or-effective position. The operator 218 normali travels with the general operator, but t 1ere is a lost-motion connection between the two, provided by the lug 219 whichprojects. below the bottom of the operator 218, said-lug being eli'ective on the forward stroke, whlle the usual second lug 123, also fast on the operator 218, is effective on the rear strokeof the general operator.

- This last-named lug 123 normally holds the supplementary operator well forward of the general operator, so that the lug 225 may be shiftedto effective position in the manner described above. AFor, this purpose said lug 123 bears against theusual comb 104. The supplementary'foperator 218 tends to travel with the general operator and for this purposeis normally heldin its rearward position by means of a spring 222, fast'to a pin 221 on the general operator and to a second pin onthe operator 218. The lug 219 during driving operation in addition has its front edge' coincide with the front edge of the general operator 120, and for this purpose there isprovided a recess 220`in the eral operator adapted to accommodate t e lug 219 and hold the front ed e thereof in line with the rest of the genera operator bar 120. t

The result of these connections is that the supplementary operator` 218 is an idle piece of mechanism in an ordinary addition operation but in a subtraction operation said supp ementary operator 218 becomes the driving mechanism or interponent through which the general operator of the machine is effective to drive the pence wheel through the necessary two digit spaces-beyond what decimal wheels have to be driven in complemental subtraction. It will be further noted that the means for obtaining the extra drive necessary in computing ten and eleven pence in addition is practically a se arate mechanism from that for producing t e two extra digit units of turning ofitle pence wheel in subtraction. When subtracting eleven pence, however, the pence wheel is not turned at all by the indexing mechanism, but is turned a single unit space by the carryover mechanism, in this manner corresponding precisely to the subtraction of nine on a decimal complementary subtraction machine, in which machines the wheel from which nine is to be subtracted is not turned, except by the carry-over mechanism. The reasons for treating ll and 9 in this way are identicahviz., that they are both the numbers from which the complements are computed. Theoretically, they are 'each the largest digits in their respective bases of computation.

In a word, when 11 on the pence dial wheel 99 appears at the sight-opening 110 and it is-desired to subtract ten pence, there will be set up in the indexing mechanism of the machine, at the depression of the 1 numeral key in tens of pence place, a condition to be subsequently utilized when the 0 key is depressed in units of pence place, as hereinbefore described. It will be noted by reference to Figs. 8 and 17 that the parts of the indexing mechanism associated with the 0 numeral key are adapted to depress the foremost pin :217 on the rack bar 143. On the forward stroke of the general-operator in subtraction, the extension 219 on the supplementar operator will engage the pin 21T to move t e rack bar 143. forwardly one digit distance to rotate -thedial wheel 99d a similar distance, bringing the numeral 0 thereon to the sight-opening 110. On the return stroke of the general operator the dial wheel 99'l will be rotated one digit distance by the carry-over mechanism, and other mechanism, hereinafter.A to be described, thus bringingthei numeral 1 on the pence wheel 99*l to the sight-opening 110, to register the .difference between ten and eleven namely, one, when subtracting ten ence from eleven pence.

Vlhen it is desired to subtract eleven nce in the above exam le, the same con 'tion will be set up in t e indexing Ymechanism when the .1 numeral key is depressed in tens of '-,pence place in the subtraction of the eleven pence. When, however, the 1 numerel key is depressed in the units of pence place in said computation of eleven pence, its associated arm 1S will swine clear of the wrist 1s on the linkage 8L which will remain idle, but its associated arm 200 will actuate the linkage 9' (Fig. 17), to restore the lever 173 on the units of pence bar 14:3 to its normal position, and thereby reset the 9 pin 94 to its normal position, so that it will not be engaged by the supplementary operator 218. It will, therefore, be noted that in the operation of subtracting eleven pence no pins on the bar 143 have been de ressed.

The escription of pence subtraction is complete except for the subtraction of nine pence, which will now be described. It has been pointed out above that to complete complementary subtraction, owing to the ditl'erence between the base 10 and base 12, it is necessary to drive the pence rack bar lll) 

